Perhaps he'd be seen as a strange anomaly. His ninja abilities are so different from the powers in the Percy Jackson world. But he could end up befriending some of the demigods and using his immortality to protect them during their dangerous quests.
He could be a mentor figure. Given his immortality and vast combat experience from the Naruto world, he could teach the demigods new ways to fight and strategize.
Percy could fit in as a strategist. His experience in dealing with various gods and monsters gives him a unique perspective on handling threats. He might suggest different approaches that the Avengers haven't thought of before, like using the environment in a more creative way, similar to how he uses water in his battles as a demigod.
She could be a new kind of demigod. Since Naruto has such strong chakra and unique abilities in her own universe, in the Percy Jackson universe, this could be seen as a new form of divine power. Maybe she is the daughter of a minor god that has some connection to ninja - like abilities. For example, a god of stealth or speed.
The oxygen tank could be a symbol of the modern world encroaching on the world of the demigods. Fanfiction writers might use it to show the contrast between the high - tech human world and the magic - filled world of Percy Jackson. It could be a source of conflict, as some demigods might be suspicious of this 'human' device, while others see it as a useful addition to their adventures.
Ice powers could fit in by being a new type of power that challenges the existing power dynamics. For instance, in battles, they could change the terrain by creating ice ramps or freezing lakes for strategic advantages.
Well, he could be a messenger in the fanfiction. Just as he is often depicted as a messenger in religious texts, he could bring important news from the celestial realm to the demigod world. Maybe he warns Percy about a new threat that is coming from a place that the demigods have no knowledge of. And his presence could stir up a lot of questions among the characters about different mythologies and how they all connect.
One way it could work is if Naruto's immortality was a result of some powerful magic in the Percy Jackson universe. Maybe he was blessed by a god or came into contact with a magical artifact that made him immortal. His ninja skills would be quite unique in that world and could make for some interesting storylines, like teaching demigods his stealth techniques.
In Percy Jackson fanfiction, Goku could be a mysterious outsider who comes to help during a great war against the Titans or some other major threat. His Saiyan fighting spirit and his various energy attacks, like the Kamehameha, could be seen as a new form of magic in that world. He might not understand all the Greek mythology stuff at first, but his pure heart and desire to do good would make him a valuable ally. For example, he could team up with Percy to fight off a horde of monsters. His super speed and strength would give them an edge in battles.
Well, Naruto has some really unique abilities like his shadow clones and chakra control. In the Marvel universe, his shadow clones could be used in a similar way to how Wolverine uses his healing factor to be in multiple places at once during a battle. His chakra control might be seen as a form of energy manipulation, like Scarlet Witch's powers but more focused on internal energy. It could add a whole new dynamic to the battles and storylines in the Marvel world.
He could be a wildcard. His lack of emotion would make his actions hard to predict. He might join a quest just because it seems logical, not because of any emotional attachment to the cause. For instance, if there's a quest to retrieve a powerful artifact, he'd analyze the risks and rewards and decide based on that, not on things like pride or loyalty like the demigods.
In fanfiction, the possibilities are endless. The demigods could introduce magic in a more widespread way in the DC Universe. Imagine Annabeth's strategic mind being used to plan against the likes of Lex Luthor. Her knowledge of architecture and ancient wisdom could give the DC heroes an edge in battles that require more than just brute force. Also, the presence of demigods could lead to new storylines about the origin of some of the DC magic - related elements.